Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).
I took a car from the Orphans' Fund Development Institution; is there usury (Riba) involved in this transaction?
If the Sharia's conditions were met, then there is no harm in this. And Allah The Exalted Knows Best.
Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?
Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.
Is it permissible for the woman who is observing Iddah after the death of her husband to exchange calls with her relatives and husband`s family call?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is permissible for the woman who is observing Iddah* after death of husband to exchange calls with them; however, when she speaks to non-Mahrams , she shouldn`t be soft of speech and she should be straight to the point. This because Almighty Allah Says (What means): "O ye wives of the Prophet! Ye are not like any other women. If ye keep your duty (to Allah), then be not soft of speech, lest he in whose heart is a disease aspire (to you), but utter customary speech." [Al-Ahzaab/32]. And Allah The Almighty Knows Best.
[1] The iddah is a waiting period that a Muslim woman observes after the death of her husband or after a divorce. The Quran says: For those men who die amongst you and leave behind wives, they (the wives) must confine themselves (spend iddah) for four months and ten days.